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...sufficient a race to the bottom and marketwide mispricing are inevitable. Underpricing occurs because bank managers and shareholders exploit mispriced deposit insurance. We show that the probability of the underpricing equilibrium increases with time since the previous market crash and that the more volatile the underlying asset market, the more likely it is subject to underpricing.
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The impact of bank lending on real estate crashes and the marketwide mispricing of real estate risk has been observed in the literature. (1) In this article, we identify the conditions under which many lenders and the conditions under which all lenders rationally choose to underprice the put option embedded in nonrecourse lending. The contribution of this article over the previous literature is the analysis of the underpricing behavior of lenders in the context of many banks and the demonstration of the competitive equilibrium in which all lenders underprice. Underpricing occurs because bank managers and shareholders exploit underpriced deposit insurance.
We construct a simple model of two competitive equilibria--"good" and "underpricing." In the good equilibrium, lenders accurately price the embedded put option, and asset prices reflect their fundamental value. In the underpricing equilibrium, lenders rationally misprice the put option. We further analyze the mechanism that leads to the economy switching between the two equilibria and study the economic conditions that make the underpricing equilibrium more likely to occur. We find that if the correctly pricing lenders cannot break even in the good state, all lenders switch to the underpricing equilibrium. The probability of entering the underpricing equilibrium increases with the value of the put option. For instance, the value of the put option is higher in more volatile asset markets, such as markets with low elasticity of supply. The probability of entering the underpricing equilibrium increases with the time since the last market crash. Markets with longer cycles are more likely to experience a higher degree of underpricing.
In the next section, we derive a model that shows that one, two or more rational lenders may choose to underprice the put option; it also shows the impact for correctly pricing lenders. The third section presents the major result of the model, showing that under certain conditions all lenders underprice. The fourth section analyzes the economic environment that makes the underpricing equilibrium more likely to occur. Implications for market outcomes are presented in the fifth section and the final section concludes.
Markets with Limited Underpricing
We assume banks are financial intermediaries that accept deposits and make loans to investors (borrowers) who purchase risky assets (properties). In this framework, Allen and Gale (1998, 1999) and Pavlov and Wachter (2004) show that correctly priced loans have no impact on asset markets. If the put option embedded in the nonrecourse loans is mispriced, however, efficient asset markets incorporate this mistake into the asset price. On its own, or in combination with other factors, this phenomenon can lead to asset-price bubbles. The previous literature does not focus on the lending behavior that could lead to this outcome. We extend this work by focusing on the lending behavior that leads to underpricing of the embedded put option. We examine the circumstances under which industry wide underpricing of the default spread is likely to occur.
We further assume that investors purchase assets each period and, following the realization of the payoff, either sell the asset and return the loan or (because these are nonrecourse loans) default. In the high payoff state, all loans are repaid. In the low payoff state, investors default and the lenders absorb the losses. (2) Thus, assets are held for one period and loans are extended for one period. Nonetheless, this is repeated over an infinite number of periods.
Following the premise that depositors are insured and, therefore, can rationally choose to remain uninformed, we assume that the cost function for each lender is:
c(y) = [y.sup.2] + 1 + vy = d(y)y + vy, (1)
where y is the number of loans made by each bank, v is the value of the put option embedded in each loan and d(y) is the deposit rate. (3) This cost function assumes that the depositors are uninformed because the deposit rate, d(y) = y + 1/y, is independent of the pricing of the credit risk by the bank. Instead, the deposit rate takes a U shape with respect to the size of the lender. Very small banks may lack brand recognition and may not offer sufficient network infrastructure, while very large banks may have to increase their deposit rates to attract customers who would otherwise prefer a different lender. (4)
The deposit rate we assume, and specifically its independence of the lending risk, is crucial for our results. We motivate this deposit rate either through assuming uninformed depositors who cannot directly lend to the users of capital or the presence of deposit insurance. Note that the deposit insurance need not be mispriced on average. Our results depend only on the assumption that the deposit insurance is independent of the lending activity of the bank. The cost of the insurance, correctly priced on average or not, becomes part of the fixed costs of lending, which are normalized to 1 in Equation (1). (5)
The second component of the cost function (1) is the value of the put option embedded in each loan times the number of loans. Because the lender provides this put option with every loan, it is part of the cost of lending....
NOTE: All illustrations and photos
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